Prime p₀= 2341128066399557129 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 28 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 90 92 120 122
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 122
Found by: Xenon
db: batch=81, k=10, 2 28 2 28 2

SPT(16)	2341127114847229699	0 72 82 118 124 174 180 222 370 412 418 468 474 510 520 592	-951552327430
STPT(10)	2341127224558346051	0 2 36 38 78 80 120 122 156 158	-841841211078
STPT(10)	2341127387465367197	0 2 12 14 72 74 132 134 144 146	-678934189932
TPT(14)	2341127913268628021	0 2 126 128 168 170 270 272 366 368 576 578 588 590	-153130929108
SPT(16)	2341127941447145339	0 14 32 90 140 158 194 212 240 258 294 312 362 420 438 452	-124952411790
SPT(16)	2341127998490870219	0 8 38 60 92 134 138 152 210 224 228 270 302 324 354 362	-67908686910
SPT(16)	2341128206791507747	0 22 120 126 136 150 172 196 336 360 382 396 406 412 510 532	140391950618
STPT(10)	2341128418868536049	0 2 18 20 30 32 42 44 60 62	352468978920
STPT(10)	2341128469193385239	0 2 18 20 30 32 42 44 60 62	402793828110
SPT(16)	2341128788690840243	0 18 30 96 156 188 198 266 270 338 348 380 440 506 518 536	722291283114
STPT(10)	2341128913041285461	0 2 6 8 48 50 90 92 96 98	846641728332